Towards a unified quantum field theory of dark energy and inflation: unstable de Sitter vacuum and running vacuum

TL;DR

This paper proposes a unified quantum field theory framework where inflation and dark energy are driven by a dynamical vacuum energy density, avoiding the need for an inflaton field and potentially resolving cosmological tensions.

Contribution

It introduces a novel approach linking inflation and dark energy through a running vacuum model driven by quantum field theory effects, without requiring an inflaton.

Findings

Inflation can be driven by $H^4$ powers in the vacuum energy density.

The model predicts a smooth transition from inflation to radiation era.

Late-time vacuum energy evolves mildly, addressing cosmological tensions.

Abstract

Inflation is a necessary cosmic mechanism to cure basic inconsistencies of the standard model of cosmology. These problems are usually `fixed' by postulating the existence of a scalar field (called the ``inflaton''). However, other less ad hoc options are possible. In the running vacuum model (RVM) framework, the vacuum energy density (VED) is a function of the Hubble rate $H$ and its time derivatives: $\rho_{\rm vac}=\rho_{\rm vac}(H, \dot{H},\ddot{H},\dots)$. In this context, the VED is dynamical (there is no rigid cosmological constant $\Lambda$). In the FLRW epoch, $\rho_{\rm vac}$ evolves very slowly with expansion, as befits the observed $\Lambda\simeq$const. behavior. In contrast, in the very early universe the vacuum fluctuations induce higher powers $H^N$ capable of unleashing fast inflation in a short period in which $H\simeq$ const. We call this mechanism `RVM-inflation'. It does not require an inflaton field since inflation is brought about by pure quantum field theory (QFT) effects on the dynamical background. It is different from Starobinsky's inflation, in which $H$ is never constant. In this work, we study a closely related scenario: the decay of the exact de Sitter vacuum into FLRW spacetime in its radiation epoch and the subsequent impact on the current universe, and compare with the RVM. We find that in both cases inflation is driven by $H^4$ powers together with subleading contributions of order $H^2$ that ease a graceful-exit transition into the radiation-dominated epoch, where the FLRW regime starts and ultimately develops a mildly evolving VED in the late universe: $\delta\rho_{\rm vac}\sim {\cal O}(m_{\rm Pl} ^2 H^2)$. The net outcome is an unified QFT approach to inflation and dark energy (conceived as dynamical vacuum energy) with potentially measurable phenomenological consequences in the present universe which can help cure the cosmological tensions.